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Published on: February 12, 2013
Rigorous computation of high-order aberrations and their errors
1Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA.
Abstract:
High-order transfer maps offer many advantages in the study of both singlepass systems, where they represent optical aberrations, and multipass systems, where they allow the direct computation of relevant properties like high-order dispersions, chromaticities, and amplitude- and parameter-dependent tune shifts. However, one remaining question is always how accurate a map of a given expansion order really is-while in many cases, the sizes of high-order contributions decrease as a function of order, this does not always have to be the case. To address these topics, we present methods to determine mathematically rigorous bounds on all missing orders beyond the one explicitly considered. The computational effort to determine these bounds is small compared to the cost of the underlying high-order transfer map computation. Furthermore, the method allows for rigorous step size control in the Differential Algebra-based integration of high-order transfer maps.
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